In this work, a new algorithm is suggested to solve the variational inequality problems for Lipschitz continuous and monotone operators and the fixed point problems for quasi-nonexpansive operators. This algorithm is constructed based on the inertial subgradient extragradient method. In addition, a strong convergence theorem for this algorithm is obtained under some extra conditions. Furthermore, an application to a signal recovery in compressed sensing problem is shown as a numerical example of the algorithm. Additionally, another example in an infinite-dimensional space is given.

中文翻译：

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一种涉及拟非膨胀算子的变分不等式问题的惯性次梯度超梯度方法及其应用

在这项工作中，提出了一种新的算法来解决 Lipschitz 连续和单调算子的变分不等式问题和拟非膨胀算子的不动点问题。该算法是基于惯性次梯度超梯度方法构建的。此外，在一些额外的条件下，得到了该算法的强收敛定理。此外，在压缩感知问题中的信号恢复的应用被显示为该算法的数值示例。此外，还给出了无限维空间中的另一个例子。